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This paper presents an investigation into solutions of two types of nonlinear Schrödinger equations of logarithmic form. This model is of particular interest to researchers due to its vast application in the field of the implication of nanofibers. Through a comprehensive analysis, it was found that the solutions take the form of Gaussian-type solitary solutions. These solutions possess a variety of new structures due to the presence of many arbitrary constants and time-dependent functions in their general expressions. By fixing these constants and functions appropriately, Gaussian solitary waves for nonlinear perturbed Schrödinger equations can be represented, which could be beneficial in understanding the dynamics of these equations in nanooptical fibers. The results obtained from this study may provide a useful tool for further research into nonlinear Schrödinger equations and can be extended to fit more applications. [ABSTRACT FROM AUTHOR]

Fractional calculus highlights its importance and has been expanded to many fields. This paper focuses on fractional integrable systems and their novel structural solutions to comply with the forefront development of nonlinear waves. Specifically, a system of fractional integrable coupled nonlinear Schrödinger (CNLS) equations are first derived from the associated linear spectral problem equipped with space-time conformable fractional derivatives of different orders. Then, by extending Darboux transformation (DT) and its generalized version to the derived fractional CNLS equations, we obtained fractional single-soliton solutions and double- and triple-semirational solutions that obey the dual power laws of independent variables. Under the dominant influences of space-time fractional orders, some novel solution structures are finally revealed based on the obtained solutions. In terms of characteristics, these spatial structures exhibit inclination, symmetry and spikes. Observing from the perspective of propagation, some of these obtained solutions have time-varying velocities and widths. From the perspective of spatiotemporal structures, some solutions form collapsed quadrangular pyramids. All of these novel solution structures cannot be supported by the integer-order CNLS equations. [ABSTRACT FROM AUTHOR]

The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics. [ABSTRACT FROM AUTHOR]

Unlike Zabusky and Kruskal who exploited the Korteweg–de Vries traveling solitons to explain the FPU-recurrence phenomenon, we consider a more robust time periodic Kuznetzov–Ma breather to resolve the paradox. The nonlinear Schrödinger equation is derived from the equation of motion of β -FPU chain, by using the method of multiple scales combined with a quasi-discreteness approximation. Modulational instability leads to the generation of a nonlinear wave of finite background, known as the Kuznetzov–Ma breather. The spatial localization and time periodic profile of the Kuznetzov–Ma breathers make it ideal in mimicking the FPU-recurrence phenomenon, as underscored by results of numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we succeed to obtain the new optical wave solutions to the truncated M-fractional (2+1)-dimensional nonlinear Schrödinger's complex hyperbolic model by utilizing the Sardar sub-equation method. The obtained solutions are in the form of trigonometric, hyperbolic and mixed form. These solutions have many applications in nonlinear optics, fiber optics, and other areas of physics and engineering where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by two-dimensional, three-dimensional and contour plots. The gained solutions are helpful for the further development of concerned model. Finally, this technique is simple, fruitful and reliable to handle the nonlinear PDEs. [ABSTRACT FROM AUTHOR]

AbstractUltra-large container ships face challenges in structural strength under complex sea conditions. The traditional equivalent design wave method inadequately considers nonlinear wave effects, leading to inaccuracies in strength assessments. This article improves the method by incorporating nonlinear wave effects and optimizing wave spectrum parameters to better simulate structural responses. A study on a container ship, using refined wave load calculations and finite element analysis, focusing on stress distribution in critical hull areas. The findings show that the enhanced method more accurately reflects real loading conditions, confirming the ship’s structural soundness and offering optimization suggestions for improved safety and longevity. [ABSTRACT FROM AUTHOR]

We present a theoretical study of the incidence of nonuniform waves between two dissipative media with finite conductivity and with a nonlinear response to the applied electric field, which is associated with the Kerr effect. From the Adler–Chu–Fano formulation, the complex propagation vectors, transmitted and reflected angles, and Fresnel coefficients are obtained for the two linear polarization states. In addition, the modification of the total internal reflection, the phase shift, the Goos–Hänchen effect, as well as the interface interaction with bright solitons are explored. Calculations are performed for fused silica, the chalcogenide As2S3 glass, and gold in glass media. [ABSTRACT FROM AUTHOR]

Nonlinear effects can enrich the propagation of elastic waves in mechanical metamaterials, which makes it possible to extend classical phenomena and functions in linear systems to nonlinear ones. In this work, rather than monochromatic waves in similar linear structures, the negative refraction is realized by mixing waves which are generated in nonlinear elastic wave metamaterials. Based on the stiffness matrix and plane wave expansion methods, dispersion curves of in–plane modes resulting from the collinear and non–linear mixings of two longitudinal waves are calculated. In the frequency spectrum, two propagating modes coalesce at exceptional points due to the coupling of in–plane modes, and those points at which the refraction type changes are also exceptional ones. Two kinds of negative refraction can be found in the mixing modes near exceptional points, but each of them needs to be induced in a specific configuration. Moreover, experiments are performed to support the pure negative refraction and beam splitting of the nonlinear elastic waves. Particularly, the parallel configuration is able to separate and extract the nonlinear mode when the single–mode negative refraction occurs, which shows the possibility to design elastic wave device by the negative refraction of nonlinear mixing waves. [ABSTRACT FROM AUTHOR]

Nonlinear wave propagation in large extra spatial dimensions (on and above d = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant F (= − (1 / 4) F μ ν F μ ν) . In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan–Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien's displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fractal nature of the local fractional Landau–Ginzburg–Higgs Equation (LFLGHE) describing nonlinear waves with weak scattering in a fractal medium. The main goal of the paper is to introduce and apply the Local Fractional Elzaki Variational Iteration Method (LFEVIM) for solution of LFLGHE. Convergence analysis of LFEVIM solution for general nonlinear local fractional partial differential equation is also provided. Two examples of the local fractional LFLGHE are considered to demonstrate the applicability of the proposed technique with numerical simulations on Cantor set. [ABSTRACT FROM AUTHOR]

This study endeavors to examine the dynamics of the generalized Kadomtsev-Petviashvili (gKP) equation in (n + 1) dimensions. Based on the comprehensive three-wave methodology and the Hirota's bilinear technique, the gKP equation is meticulously examined. By means of symbolic computation, a number of three-wave solutions are derived. Applying the Lie symmetry approach to the governing equation enables the determination of symmetry reduction, which aids in the reduction of the dimensionality of the said equation. Using symmetry reduction, we obtain the second order differential equation. By means of applying symmetry reduction, the second order differential equation is derived. The second order differential equation undergoes Galilean transformation to obtain a system of first order differential equations. The present study presents an analysis of bifurcation and sensitivity for a given dynamical system. Additionally, when an external force impacts the underlying dynamic system, its behavior resembles quasi-periodic phenomena. The presence of quasi-periodic patterns are identified using chaos detecting tools. These findings represent a novel contribution to the studied equation and significantly advance our understanding of dynamics in nonlinear wave models. [ABSTRACT FROM AUTHOR]

We focused on solitonic phenomena in wave propagation which was extracted from a generalized breaking soliton system in (3 + 1)-dimensions. The model describes the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. Abundant double-periodic soliton, breather wave and the multiple rogue wave solutions to a generalized breaking soliton system by the Hirota bilinear form and a mixture of exponentials and trigonometric functions are presented. Periodic-soliton, breather wave and periodic are studied with the usage of symbolic computation. In addition, the symbolic computation and the applied methods for governing model are investigated. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of double-periodic soliton and breather wave solutions are explained all right. The findings demonstrate the investigated model's broad variety of explicit solutions. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering. [ABSTRACT FROM AUTHOR]

The present work deals with the investigation of the time‐fractional Klein–Gordon (K‐G) model, which has great importance in theoretical physics with applications in various fields, including quantum mechanics and field theory. The main motivation of this work is to analyze modulation instability and soliton solution of the time‐fractional K‐G model. Comparative studies are investigated by β‐fraction derivative and M‐fractional derivative. For this purpose, we used unified and advanced exp(−ϕ(ξ))‐expansion approaches that are highly important tools to solve the fractional model and are used to create nonlinear wave pattern (both solitary and periodic wave) solutions for the time‐fractional K‐G model. For the special values of constraints, the periodic waves, lumps with cross‐periodic waves, periodic rogue waves, singular soliton, bright bell shape, dark bell shape, kink and antikink shape, and periodic wave behaviors are some of the outcomes attained from the obtained analytic solutions. The acquired results will be useful in comprehending the time‐fractional K‐G model's dynamical framework concerning associated physical events. By giving specific values to the fractional parameters, graphs are created to compare the fractional effects for the β‐fraction derivative and M‐fractional derivative. Additionally, the modulation instability spectrum is expressed utilizing a linear analysis technique, and the modulation instability bands are shown to be influenced by the third‐order dispersion. The findings indicate that the modulation instability disappears for negative values of the fourth order in a typical dispersion regime. Consequently, it was shown that the techniques mentioned previously could be an effective tool to generate unique, precise soliton solutions for numerous uses, which are crucial to theoretical physics. This work provided the effect of the recently updated two fraction forms, and in the future, we will integrate the space–time M‐fractional form of the governing model by using the extended form of the Kudryashov method. Maple 18 is utilized as the simulation tool. [ABSTRACT FROM AUTHOR]

Of current interest, there have recently appeared a series of the shallow-water papers in Mod. Phys. Lett. B. Illuminated by those papers and to make the story more complete, for the nonlinear long waves in the shallow water, this paper is scheduled to investigate a (2+1)-dimensional generalized Broer-Kaup system. As for the wave height and wave horizontal velocity, we employ symbolic computation, with the view of constructing out two groups of the similarity reductions. [ABSTRACT FROM AUTHOR]

In data assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is computationally expensive and infeasible to run in real-time for complex systems. Here, we present a novel particle filter methodology, the Deep Latent Space Particle filter or D-LSPF, that uses neural network-based surrogate models to overcome this computational challenge. The D-LSPF enables filtering in the low-dimensional latent space obtained using Wasserstein AEs with modified vision transformer layers for dimensionality reduction and transformers for parameterized latent space time stepping. As we demonstrate on three test cases, including leak localization in multi-phase pipe flow and seabed identification for fully nonlinear water waves, the D-LSPF runs orders of magnitude faster than a high-fidelity particle filter and 3-5 times faster than alternative methods while being up to an order of magnitude more accurate. The D-LSPF thus enables real-time data assimilation with uncertainty quantification for the test cases demonstrated in this paper. [ABSTRACT FROM AUTHOR]

In this work, exact solutions of the (3+1) dimensional Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation have been produced by applying the modified sub-equation method, which is reliable and effective among analytical methods. This equation is a wavelet equation that describes non-linear and dispersive wave propagation. The aim of considering this model is to model non-linear and dispersive interactions in an environment and enable their analysis by analytical methods. By applying this method, different wave solution classes in hyperbolic and rational forms are obtained. The graphs of solitary waves produced are in 2D, 3D and contour types. In this study, computer package programs have been used for complex operations and drawing graphics. [ABSTRACT FROM AUTHOR]

The higher harmonics generated by nonlinear sheath motion would enhance the standing wave effect, and thus lead to center-peaked plasma density profile in very-high-frequency (VHF) capacitive discharges. In this work, a nonlinear transmission line (NTL) model introduced in Zhou et al (2021 Plasma Sources Sci. Technol. 30 125017) has been extended, with radial transport of various particles and nonlinear sheath motion into account, to investigate the effects of CF4 fraction α on the nonlinear standing wave excitation and plasma radial uniformity in VHF (60 MHz) capacitively coupled Ar/CF4 plasmas at 3 Pa. The results indicate that for pure Ar discharges (i.e. α = 0%), the nonlinearly excited harmonics with short wavelength significantly enhance the electron power absorption at the radial center, resulting in a pronounced central-high plasma density profile. As α increases, the high-order harmonics are gradually damped due to the increase of resistance, as well as the longer wavelength caused by thicker sheath thickness. Thus, the radial profile of the electron absorbed power density shifts from center-peak to edge-high. Besides, at the radial center, the electron density and Ar+ ion density decrease with α , CF3+ ion density shows an increasing trend, while F− ion density initially rises and then decreases. Moreover, the density profiles of all the species become more uniform at higher CF4 fraction, due to the suppressed nonlinear standing wave excitation and the longer wavelength of the nonlinear harmonics. [ABSTRACT FROM AUTHOR]

When an ultrasonic pulse propagates in a thin plate, nonlinear Lamb waves with higher harmonics and a zero-frequency component (ZFC) will be generated because of the nonlinearity of materials. The ZFC, also known as the static displacement or static component, has its unique application on the evaluation of early-stage damages in the elastic symmetrical undulated plate. In this study, analysis of the excitation mechanism of the ZFC and the second harmonic component (SHC) was theoretically and numerically investigated, and the material early-stage damage of a symmetrical undulated was characterized by studying the propagation of nonlinear Lamb waves. Both the ZFC and SHC can be effectively employed in monitoring the material damages of the undulated plate in its early stage. However, several factors must be considered for the propagation of the SHC in an undulated plate because of the geometric curvature and interference between the second harmonics during propagation, preventing efficient application of this technique. If the fundamental wave can propagate in the plate regardless of the plate boundary conditions, an accumulative effect always exists for the ZFC in a thin plate, indicating that the ZFC is independent of the structural geometry. This study reveals that the ZFC-based inspection technique is more efficient and powerful in characterizing the damages of a symmetrical undulated plate in the early stage of service compared to the second harmonic method. [ABSTRACT FROM AUTHOR]

Accurate surface wave prediction can potentially improve the safety and efficiency of various offshore operations, such as heavy lifts and active control of wave energy converters and floating wind turbines. Prediction of surface waves, even if only for a few periods in advance, is of value for decision-making. This study aims to predict weakly nonlinear surface waves (up to the second-order) in real-time using a data-driven model based on artificial neural networks (ANNs), where the application of physics is investigated to aid the development of a data-driven model. Based on numerically synthesized nonlinear wave records calculated using exact second-order theory, ANN models were trained to separate the nonlinear bound components at an up-wave location, propagate the linear waves, and reintroduce the nonlinear components as a correction to the prediction at a down-wave location. Our findings indicate that the optimal approach is to predict each stage separately following the basic physical structure of weakly nonlinear water waves using a series of ANN rather than direct prediction in a single step using ANN. Furthermore, we examined the generalization of the models across different sea states and investigated the impact of the second-order bound waves on prediction accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a three-wave resonant interaction system, which describes the mixture of waves with different frequencies in a weakly nonlinear and dispersive medium, is investigated with the help of the Darboux transformation and its extension. Firstly, we construct the dark–bright–bright mixed multi-soliton solutions in terms of the determinant. Dark–bright–bright solitons are found to arise in the focusing, defocusing and mixed cases. Bound state of the two dark–bright–bright solitons is also analyzed. Secondly, we derive the dark–bright–bright mixed high-order semi-rational solitons and find that their structures are different from the multi-soliton ones. Finally, we present the Nth-order breather solutions in terms of the determinant, where N is a positive integer. Line-shaped and three wing-shaped structures of the breathers are obtained. [ABSTRACT FROM AUTHOR]

Nonlinear electrostatic waves on the ion time scale have been studied in a quantum magnetoplasma in the presence of relativistically degenerate electrons. In this regard, Zakharov Kuznetsov (ZK) equation has been derived using the reductive perturbation technique. The single and two soliton solutions of the ZK equation have been obtained by employing Hirota formalism. The nonrelativistic and ultrarelativistic limits of the relativistically degenerate electrons have been studied and discussed in detail for important plasma parameters both for the single and two soliton solutions of the ZK equation. We have applied our study for the plasma parameters that are found in the white dwarfs. It has been noticed that the interaction of the ZK solitons depends on the propagation vectors in the predominant direction of propagation. Importantly, it has been found that the spatial and temporal scales over which the interaction of solitons occur are different for the nonrelativistic and ultrarelativistic cases. [ABSTRACT FROM AUTHOR]

The diagnostic of magnetized radio frequency complex plasma via probing techniques and spectroscopy is challenging. However, a self-excited dust ion acoustic waves (DIAWs) have been observed employing laser scattering. Inspired by the current high enthusiasm for the theoretical description of complex plasma, we study the propagation of DIAWs in a three-dimensional collisional and magnetized dusty plasma medium. We consider the fluid model for dust and ion particles, while we neglect the inertia of electrons considering the Boltzmann distribution. A linear dispersion relation is obtained and a nonlinear modified Zakharov–Kuznetsov equation is derived utilizing the reductive perturbation technique. The effects of ion-neutral and dust-neutral collisions on the dynamics of the nonlinear DIAWs are considered. The phase portrait analysis and numerical illustration of a rarefactive DIA cnoidal waves and solitons are also presented. Our findings agree with experimental observations by Choudhary M, Bergert R, Mitic S, and Thomas MH. [Influence of external magnetic field on dust acoustic waves in a capacitive rf discharge. Contrib Plasma Phys. 2020;60:e201900115] as the growth of nonlinear periodic waves is recorded when the magnetic field is roughly 0.05 T and vanishes when the magnetic field is close to 0.1 T. Moreover, the model reveals that the electrostatic cnoidal and soliton waves propagate with low frequencies up to 140 Hz. [ABSTRACT FROM AUTHOR]

Bifurcations of nonlinear and supernonlinear ion-acoustic waves (IAWs) are studied in an electron-ion plasmas with generalized (r, q)-distributed electrons. The IAWs are examined under the Zakharov–Kuznetsov (ZK) and modified ZK equations using the reductive perturbation technique. Transforming both the ZK and mZK equations into their corresponding dynamical systems, all possible phase spaces and potential energy functions are analyzed. The nonlinear periodic and solitary wave solutions are obtained under the ZK and mZK equations. A newly discovered supernonlinear wave, in particular, supernonlinear periodic wave under the modified ZK equation in electron-ion magnetized plasma with (r, q)-distributed electrons is reported for the first time in the literature. Nonlinear and supernonlinear wave solutions are shown under the influence of physical parameters. The proposed study contributes to new wave motions in slow solar wind streams and astrophysical plasmas. [ABSTRACT FROM AUTHOR]

The existence and propagation of dust acoustic waves in quantum four-component plasma are investigated by employing Sagdeev pseudo-potential. The plasma under consideration consists of both quantum electrons and ions beside negative and positive dust particulates. The general determining equation of the Sagdeev pseudo-potential is obtained, and it is found that the equation is very difficult to integrate. Due to the complexity involved in the structure of Sagdeev potential, this equation can only be solved in some limiting cases, such as semi-classical limit and small amplitude approximation. Our findings support the existence of compressive, rarefactive solitary waves and double layers in our plasma system. The influence of the relevant plasma parameters on the existence and profile of the obtained quantum nonlinear waves has been studied. The implications of the obtained results have wide relevance in the study of space and laboratory quantum dusty plasmas situations such as Jupiter's magnetosphere, upper and lower mesosphere, and comet tails, as well as in condensed matter systems. [ABSTRACT FROM AUTHOR]

In a recent paper Li et al. (Z Angew Math Phys 73:52, 2022. https://doi.org/10.1007/s00033-022-01681-4) have considered a generalized nonlinear Schrödinger equation which has extensive applications in various fields of physics and engineering. After proving Liouville integrability of this equation, they investigated the phenomenon of the modulational instability for the possible reason of the formation of the rogue waves. By means of the generalized ( 2 , N - 2 )-fold Darboux transformation, authors presented several mixed localized wave solutions, such as breathers, rogue waves and semi-rational solitons for their model equation, and accurately analyzed a number of important physical quantities. It is the aim of this Comment to point out that (i) the baseband modulation instability was developed in a wrong way and (ii) one of the two different types of Taylor series expansions for solution of Lax pair used in that article for building analytical solutions, especially the one obtained with ξ j = Z does not correspond to any solution of the spectral problem (2.1) when using u 0 x , t as the seed solution. Consequently, all mixed localized solutions that involve the mentioned Taylor series are invalid. [ABSTRACT FROM AUTHOR]

We derive a nonlinear acoustic wave propagation model for analyzing the thermoviscous dissipation of nonlinear acoustic waves in narrow pores with wavy walls using the boundary layer theory. As a nonlinear acoustic wave propagates in a pore, the wave-steepening effect competes with the bulk dissipation, as well as the thermoviscous heat transfer and shear from the pore walls. Due to thermoviscous dissipation, the wave thickness increases beyond the weak shock thickness scale. Using the weak shock thickness scale, we obtain dimensionless linear and nonlinear model wave equations governing the shock–wall interactions. We also perform two-dimensional shock-resolved direct numerical simulation of the wave propagation inside the pores and compare the results with model equations. The direct numerical simulation and model calculations show that, for flat walls and shock strength parameter ϵ, the dimensional wall heat-flux and shear scale as ϵ. For wavy walls, the scaling becomes ϵ 3 / 2 − n (k) where k is the wall-waviness wavenumber and the exponent n increases from 0.5 for k = 0 to n (k) ≈ 0.65 for k = 10, n (k) ≈ 0.75 for k = 20, and n (k) ≈ 0.85 for k = 40. Furthermore, we show that both the dimensionless scaled wall shear and wall heat-flux decrease with increasing k. [ABSTRACT FROM AUTHOR]

The objective of this research is to demonstrate the effectiveness of a phased array-based nonlinear wave mixing technique to characterize internal, localized microscale damage in an additively manufactured (AM) component. By using phased arrays for the generation of the incident waves, it is possible to produce a nonlinear wave mixing scanning technique without the need for immersion or changing coupling conditions. The phased arrays can be configured to generate incident waves in multiple directions that meet the resonance conditions required for nonlinear wave mixing at a variety of internal locations. This allows for the scanning of a specimen without the removal and re-coupling of the source transducers, leading to greater scanning speed and repeatability. To demonstrate the accuracy of this phased array wave mixing approach, measurements of acoustic nonlinearity in an AM component are first made with a bulk wave second harmonic generation through thickness measurement. Next, nonlinear wave mixing measurements are made with single element transducers to confirm the sensitivity of the proposed nonlinear wave mixing approach to lack-of-fusion porosity in AM metals. Finally, phased arrays are used to highlight the effectiveness of the proposed nonlinear wave mixing technique in these same AM components. [ABSTRACT FROM AUTHOR]

We investigate the behavior of nonlinear waves in the Hall-magnetohydrodynamics model of non-ideal fluids with the van der Waals equation of state. It is shown that the Hall effect leads to the formation of a nonclassical shock wave that does not follow Oleinik's entropy condition and propagates as an undercompressive shock. The evolution of a rectangular pulse is discussed by solving a Riemann problem with initial data containing a pair of discontinuities. In particular, we provide a thorough discussion of interaction of various waves emerging from the discontinuities. It is observed that during this interaction, a nonclassical shock may transform into a classical sonic shock depending on the critical value of the Hall parameter. Furthermore, we analyze the effects of van der Waals parameters and the Hall parameter on various aspects of wave propagation, such as shock speed, shock strength, width of wave fan, and interaction time. [ABSTRACT FROM AUTHOR]

This research is the first attempt to examine the hydrodynamic loads of nonlinear solitary waves on bridge decks near a coastline. We employ laboratory experiments and a large eddy simulation model to simulate the wave motion and wave loads on a partially submerged rectangular deck near a sloped beach. The measured wave heights and wave loads from wave flume experiments verify the accuracy of the computational fluid dynamics model. A series of parametric studies investigates the effects of wave height, submergence, and beach slope on the wave loads of the bridge deck. The simulation results revealed that the hydrodynamic forces are linearly proportional to the wave height, and the dimensionless force coefficients depend on the submergence ratio and beach slope. For the mild slope case (θ = 18.5°), the wave load during the run-up stage is larger than that during the run-down stage. The largest drag coefficient CD = 0.58, lift coefficient CL = 0.45, and pitch moment coefficient Cm = −0.21 occur when the deck is initially above the still wave level. On a steeper slope (θ = 30°), the run-down current could generate a large downward force and a clockwise moment when the bridge deck is close to a shoreline. Hereafter, coastal bridges should consider the impact of the run-down flow during tsunamis and storm surges. [ABSTRACT FROM AUTHOR]

We study bifurcations of nonlinear waves (spatially inhomogeneous solutions) emerging from homogeneous equilibrium states of an initial boundary value problem, arising in nonlinear optics, for a nonlinear parabolic equation on a disk with a spatial argument rescaling operator and with time delay. In the plane of the main parameters of the equation, we construct stability (instability) domains of homogeneous equilibrium states and study the dynamics of the stability domains depending on the rescaling coefficient. We investigate the mechanisms of stability loss by homogeneous equilibrium states, the possible bifurcations of spatially inhomogeneous self-oscillatory solutions, and their stability. We demonstrate the possibility of bifurcation of stable rotational and spiral waves. [ABSTRACT FROM AUTHOR]

Optical nonlinearities are one of the most fascinating properties of two-dimensional (2D) materials. While tremendous efforts have been made to find and optimize the second-order optical nonlinearity in enormous 2D materials, opportunities to explore higher-order ones are elusive because of the much lower efficiency. Here, we report the giant high odd-order optical nonlinearities in centrosymmetric correlated van der Waals insulator manganese phosphorus triselenide. When illuminated by two near-infrared femtosecond lasers, the sample generates a series of profound four-and six-wave mixing outputs. The near-infrared third-order nonlinear susceptibility reaches near the highest record values of 2D materials. Comparative measurements to other prototypical nonlinear optical materials [lithium niobate, gallium(II) selenide, and tungsten disulfide] reveal its extraordinary wave mixing efficiency. The wave mixing processes are further used for nonlinear optical waveguide with multicolor emission. Our work highlights the promising prospect for future research of the nonlinear light-matter interactions in the correlated 2D system and for potential nonlinear photonic applications. [ABSTRACT FROM AUTHOR]

This study examines the (3 + 1) dimensional extended quantum Zakharov–Kuznetsov equation in weakly nonlinear ion-acoustic phenomena and quantum electron-positron-ion magneto plasma. For accomplishing this goal, two distinct mathematical approaches namely new mapping method and new Kudryashov's method are fashioned. These solutions encompass dark, bright, singular, periodic singular, and some other rational solutions. Graphical depictions of some obtained solutions by 2D, 3D and contour plots meticulously crafted within figures offered profound insights into the deep physical appearances of the structures under examination. Our outcomes highlight that the proposed methods assist as an efficient and inclusive approaches to discover the solitons for the present model. The comparison with previous papers highlights that the methods employed in our study are being utilized for the first time within the context of the extended quantum Zakharov–Kuznetsov equation which underscores the novelty of our paper. By retaining these two methods, we not only boost our consideration of the dynamical behavior of these kind of models but also provide a useful tool for finding specific soliton solutions of nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

In this research, we use several ansatz transformations to study analytical solutions of different nonlinear waves (such as lump soliton, periodic waves, multi-waves, lump one kink, and lump two kink) for a well-known model, the Landau–Ginzburg–Higgs model. The Landau–Ginzburg–Higgs (LGH) model combines concepts from particle physics and condensed matter physics to describe phase transitions and symmetry-breaking processes. It integrates the particle physics concepts of the Higgs mechanism, the Landau theory of phase transitions, and the Ginzburg-Landau theory of superconductivity. A lump soliton is a confined wave phenomenon that travels through a medium without changing form or amplitude. These solitons are produced in a variety of nonlinear systems, including optical fibers and some kinds of fluid dynamics equations, where they are essential for transferring energy and information. Periodic waves are defined by consistent, recurring oscillation patterns in both space and time. These waves are essential to many technology applications and natural phenomena, such as electromagnetic radiation and ocean waves. A confined wave disturbance with a single sudden shift in amplitude is referred to as a soliton with one kink, or single-kink soliton. A soliton with two kinks is a solution for a solitary wave that has two localized areas where the wave profile bends or alters abruptly. The solutions are graphically displayed using contour, 3D, and 2D graphs. [ABSTRACT FROM AUTHOR]

This article utilizes the Lie symmetry method to analyze the (n + 1) -dimensional modified Zakharov–Kuznetsov (mZK) equation, which characterizes weakly nonlinear traveling waves in plasma with a constant magnetic field, comprising cold ions and hot isothermal electrons. The model is also applicable to dusty and magnetized plasma. Lie point symmetries and associated group invariant solutions are computed using Lie group theory, with the underlying equation. The improved tan ( Φ (ξ) 2) -expansion method is then employed to derive soliton solutions, including hyperbolic, trigonometric, rational, and exponential forms. Graphic interpretations of specific solutions are provided. Nonlinear self-adjointness is used to compute non-local conservation laws in lower dimensions, and conservation laws are developed based on the equation's formal Lagrangian structure, applying Ibragimov's theorem. These findings highlight the novelty and reliability of the methodology employed. [ABSTRACT FROM AUTHOR]

The paper introduce a novel auxiliary equation method for the successful derivation of traveling wave solutions for the non-linear Kairat-X (K-X) equation. Along with other novel results, soliton, singular, triangular periodic, and doubly periodic topological solutions are among the solutions obtained. The study revisits the concept of optical solitary waves, enhancing our understanding of the model. Previous studies have already derived analytical solutions using diverse approaches, contributing to the discovery of new soliton solutions within this framework. These solutions are characterized through three-dimensional, contour plot, and two-dimensional profile analyses. Additionally, the impact of time on the propagation of wave patterns is explored. The outcomes show how well our suggested approach works to solve non-linear evolution equations by producing fresh, more thorough solutions, making it a powerful mathematical tool for doing so. Through this article, we elucidate how leveraging NAEM with the Kairat-X equation can lead to optimized optical systems, improved data transmission rates, and the evolution of nonlinear optics towards more efficient and reliable communication technologies. [ABSTRACT FROM AUTHOR]

The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is used to characterize the nonlinear behavior of magnets and describe how ferromagnetic materials are ordered is the main subject of this investigation. The system's dynamics are governed by the Schrödinger equation, which explains the variations in its quantum state over time. We implement two modern and efficient techniques, the improved auxiliary equation scheme, and the improved tanh method to find the exact solutions of HSFC model and develop travelling wave solutions in terms of rational, trigonometric, and hyperbolic functions with arbitrary parameters. Numerical findings are shown in 3-D plots, 2-D curves, and contours with carefully selected parametric values used to illustrate the dynamic wave shape using MATLAB software. The acquired results provide important insights into the physical implications of nonlinear dynamics in magnetic systems and significantly contribute to the understanding of electromagnetic wave models. The article finishes with a thorough appraisal of the physical interpretations generated from the obtained results. [ABSTRACT FROM AUTHOR]

Under the consideration of computational software Mathematica on the basis of extended simple equation method, constructed the periodic wave soliton solutions for nonlinear Zakharov–Kuznetsov modified equal width equation. In this study, constructed soliton solutions included periodic singular solitons, bright solitons, kink solitons, anti-kink solitons, travelling waves, dark solitons and solitary waves are more interesting, prices and some are novel. The graphical demonstration of some investigated results shown by contour, 2-dim and 3-dim by computing software Mathematica under numerical simulation to visualizing the physical phenomena of obtained results. The demonstrated results will be helpful in the study of nonlinear phenomena in various kinds of domains including nonlinear optics, nonlinear dynamics, solitons wave theory, optical fiber, nonlinear acoustic wave, communications system, networking system and transmission of signals. The extended simple equation technique is a concise, straightforward, powerful and reliable approach for the investigation of different kinds of nonlinear partial evolution equations. [ABSTRACT FROM AUTHOR]

A pseudopotential analysis is presented for the propagation of nonlinear periodic dust-acoustic waves in a dusty plasma comprising cold negative dust, Boltzmann electrons, and Boltzmann or Cairns nonthermal positive ions, extending thus earlier treatments for ion-acoustic waves in electron–proton plasmas. The dusty plasma model where both electrons and ions are Boltzmann does not admit solitons, but works for nonlinear periodic waves. For consistency in the periodic case, two properties are required: conservation per cycle of species densities and that for very small amplitudes the waves resemble linear waves. The first property has to be imposed through a global perturbation of the undisturbed equilibrium, whereas the second property follows naturally from the formalism. After obtaining the general analytical methodology, a numerical analysis is discussed and illustrated with graphs for the electrostatic potential profile, the Sagdeev pseudopotential, the wave electric field, and the three different species densities, first for the Boltzmann and thereafter for the Cairns ions. [ABSTRACT FROM AUTHOR]

In this study, within the framework of electron magnetohydrodynamics, taking into account thermomagnetic phenomena, we obtained a new large-scale instability of the α -effect type, which ensures the generation of large-scale vortex and magnetic fields. This instability occurs in a flat layer of temperature-stratified plasma under the influence of an external uniform magnetic field inclined relative to the layer, combined with a small-scale external force having zero helicity. The external force is presented as a source of small-scale oscillations in the speed of electrons with a low Reynolds number R ≪ 1. The presence of a small parameter in the system allowed us to apply the method of multiscale asymptotic expansions to derive nonlinear equations for vortex and magnetic disturbances. These equations were obtained in third-order Reynolds number. Using solutions for the velocity field in zero order in Reynolds number, we determined the average helicity H = v 0 · rot v 0 ¯ and its relation to the α -effect. A necessary condition for the generation of average helicity in stratified magnetized plasma is the inclined orientation of the external magnetic field and the presence of a small-scale force. A new effect related to the influence of thermal force (the Nernst effect) on large-scale instability is discussed. It is shown that an increase in the Nernst parameter leads to a decrease in the amplification factor α and thereby prevents the development of large-scale instability. With the help of numerical analysis, stationary solutions to the vortex and magnetic dynamo equations in the form of localized structures like nonlinear waves of the Beltrami were obtained. [ABSTRACT FROM AUTHOR]

In this study, the underlying traits of the new wave equation in extended (3+1) dimensions, utilized in the field of plasma physics and fluids to comprehend nonlinear wave scenarios in various physical systems, were explored. Furthermore, this investigation enhanced comprehension of the characteristics of nonlinear waves present in seas and oceans. The analytical solutions of models under consideration were retrieved using the sub-equation approach and Sardar sub-equation approach. A diverse range of solitons, including bright, dark, combined dark-bright, and periodic singular solitons, was made available through the proposed methods. These solutions were illustrated through visual depictions utilizing 2D, 3D, and density plots with carefully chosen parameters. Subsequently, an analysis of the dynamical nature of the model was undertaken, encompassing various aspects such as bifurcation, chaos, and sensitivity. Bifurcation analysis was conducted via phase portraits at critical points, revealing the system's transition dynamics. Introducing an external periodic force induced chaotic phenomena in the dynamical system, which were visualized through time plots, twodimensional plots, three-dimensional plots, and the presentation of Lyapunov exponents. Furthermore, the sensitivity analysis of the investigated model was executed utilizing the Runge-Kutta method. The obtained findings indicated the efficacy of the presented approaches for analyzing phase portraits and solitons over a wider range of nonlinear systems. [ABSTRACT FROM AUTHOR]

The wave motions of the initial discontinuities in the inviscid shallow water wave model governed by the bad Jaulent-Miodek system are explored by the Whitham modulation theory and dynamical analysis. The $ N $-phase algebro-geometric solutions along with the related genus-$ N $ Whitham equations are derived by algebro-geometric method and Flaschka-Forest-McLaughlin approach, respectively. The complete classification of solutions to the bad Jaulent-Miodek system is carried out by solving the Whitham equations both theoretically and numerically. Some exotic phenomena of nonlinear wave motions such as rarefaction waves and dispersive shock waves are found in the inviscid shallow water. Particularly, the nonlinear wave motions including the two-phase algebro-geometric solutions are found in the inviscid shallow water wave. It is shown that the results from Whitham modulation theory agree very well with the numerical calculations and dynamical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we shall investigate the large-time behavior of the solution to an outflow problem of the one-dimensional bipolar quantum Navier-Stokes-Poisson system in the half space. Under some suitable assumptions on the boundary data and the space-asymptotic states, we successfully construct a nonlinear wave which is the superposition of the stationary solution and the 2-rarefaction wave. Then, by means of the $ L^2 $-energy method, we prove that this nonlinear wave is asymptotically stable provided that the initial perturbation and the strength of the stationary solution are small enough, while the strength of the 2-rarefaction wave can be arbitrarily large. [ABSTRACT FROM AUTHOR]

Terahertz (THz) waves have exhibited promising prospects in 6G/7G communications, sensing, nondestructive detection, material modulation, and biomedical applications. With the development of high-power THz sources, more and more nonlinear optical effects at THz frequency and THz-induced nonlinear optical phenomena are investigated. These studies not only show a clear physics picture of electrons, ions, and molecules but also provide many novel applications in sensing, imaging, communications, and aerospace. Here, we review recent developments in THz nonlinear physics and THz-induced nonlinear optical phenomena. This review provides an overview and illustrates examples of how to achieve strong THz nonlinear phenomena and how to use THz waves to achieve nonlinear material modulation. [ABSTRACT FROM AUTHOR]

Ultra‐low frequency (ULF) waves contribute significantly to the dynamic evolution of Earth's magnetosphere by accelerating and transporting charged particles within a wide energy range. A substantial excitation mechanism of these waves is their drift‐bounce resonant interactions with magnetospheric particles. Here, we extend the conventional drift‐bounce resonance theory to formulate the nonlinear particle trapping in the ULF wave‐carried potential well, which can be approximately described by a pendulum equation. We also predict the observable signatures of the nonlinear drift‐bounce resonance, and compare them with spacecraft observations. We further discuss potential drivers of the pendulum including the convection electric field and the magnetospheric dayside compression, which lead to additional particle acceleration or deceleration depending on magnetic longitude. These drivers indicate preferred regions for nonlinear ULF wave growth, which are consistent with previous statistical studies. Plain Language Summary: In Earth's magnetosphere, electromagnetic oscillations in the mHz frequency range referred to as ultra‐low frequency (ULF) waves have been frequently reported in space and ground‐based observations. These waves have been known to interact resonantly with magnetospheric particles during their drift and bounce motions, which plays a key role in the acceleration and transport of charged particles in the Van Allen radiation belts. Drift‐bounce resonance occurs when a resonant particle experiences repetitive patterns of the wave field over consecutive bounce cycles along its drift orbit, thus enabling a cumulative energy exchange between waves and particles. In previous studies of drift‐bounce resonance, a linearization approach is applied for simplicity. Here, we extend the conventional theory into the nonlinear regime, to formulate the nonlinear trapping of particles based on a pendulum equation and to predict the characteristic signatures of drift‐bounce resonance. Moreover, we discuss the potential drivers of the pendulum, including the magnetospheric convection and the dayside compression, which break the symmetry in the phase portrait of the particle trajectories and therefore, lead to continuous particle acceleration or deceleration depending on magnetic longitude. Our study on nonlinear drift‐bounce resonance is helpful to the understanding of the ULF wave‐particle interactions and the wave excitation processes. Key Points: A nonlinear framework for drift‐bounce resonance is developed to describe the particle behavior in Ultra‐low frequency (ULF) wavesNonlinear drift‐bounce resonance is characterized observationally by rolled‐up structures in particle pitch angle spectrumOur theory predicts that dayside and dusk sectors are preferred regions for nonlinear ULF wave growth [ABSTRACT FROM AUTHOR]

This paper presents a discussion on observations of nonlinear internal waves (NLIWs) in the coastal zone of the Sea of Japan, based on the mooring of thermostring clusters in different seasons of 2022. For statistical evaluation of the frequency of event occurrence and determination of NLIW movement direction, we use our observations of the past 12 years. We present the NLIW structures, observed in spring, summer, and autumn of 2022, which are typical for this shelf area. Two types of nonlinear waves are described—solitary and undular bores, with or without strong vertical mixing behind the front. We demonstrate spatial transformation of an undular bore as it moves over the shelf. A mathematical model based on the second-order shallow water approximation is proposed for numerical simulation. To simplify calculations, the authors limit themselves to two- and three-layer shallow water models. We investigate the possibility of spatiotemporal reconstruction of internal nonlinear structures between thermostrings using experimental data and proposed models. The authors show that at distances of up to several kilometers between thermostrings, the wave fields of strongly nonlinear and nonstationary structures can be successfully reconstructed. Water flow induced by NLIWs can be reconstructed from the data of even one thermostring. [ABSTRACT FROM AUTHOR]

In this paper, the new modification of the Sardar sub-equation method is used to generate a wide variety of exact solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky system. We focus on investigating the Konopelchenko–Dubrovsky equation, which serves as a mathematical model for studying nonlinear waves in the field of mathematical physics. This equation specifically captures the behavior of waves with weak dispersion, allowing us to explore the intricate dynamics and characteristics associated with such wave phenomena. By delving into the properties and solutions of this system, we aim to deepen our understanding of nonlinear wave propagation and its implications in the broader field of mathematical physics. The exact solutions generated through this modified method provide valuable insights into the propagation and interaction of waves with weak dispersion in the system. The obtained novel solutions are expressed as hyperbolic, and trigonometric functions. The proposed model successfully constructs various types of solutions, including singular, dark, bright, trigonometric, periodic, dark–bright, exponential, and hyperbolic. These solutions are presented with appropriate parameter values in both 3D and 2D graphics. [ABSTRACT FROM AUTHOR]

In this paper, we primarily focus on the nonlinear paraxial wave equation in Kerr media, a generalization of the nonlinear Schrödinger equation utilized to characterize the dynamics of optical beam propagation. By using three potent analytical methods, namely, the Sine-Gordon expansion method, the functional variable method, and the Bernoulli (G′/G)-expansion method, numerous novel soliton solutions are derived. These solutions, comprising hyperbolic, trigonometric and exponential functions, represent significant additions to the field of optics. Furthermore, we elucidate the physical characteristics of these novel optical soliton solutions by presenting a series of three-dimensional (3D) and two-dimensional (2D) graphs with appropriate parameter values. [ABSTRACT FROM AUTHOR]

In this research, the modified extended tanh-function (METF) and the extended Jacobi elliptic function expansion (EJEFE) techniques are used to investigate the generation and detection of soliton structures in the Hirota–Maccari (HM) model. Consequently, we obtain soliton solutions with advanced structures, including singular bright soliton, dark soliton, periodic waves, breather waves, periodic breather waves, and multiple bright and dark breather waves. In addition, a lump-type breather wave is also included in the presented solutions. Stability analysis of the obtained solutions is addressed by employing the Hamiltonian technique. 3D surfaces and 2D visuals of the outcomes are represented with the help of a computer application. These findings contribute to understanding nonlinear wave phenomena with potential applications in optics, fluid dynamics, and plasma physics. [ABSTRACT FROM AUTHOR]

This paper proposes abundant accurate wave solutions that represent the plasma wave propagation based on crystal lattice theory and physicochemical characterization. The Gilson–Pickering () model is analytically and numerically solved by two recent techniques. This model is a basic unidirectional wave propagation model that describes the prorogation of waves in crystal lattice theory and plasma physics. The investigated model has a deep connection with some nonlinear evolution equations under specific values of its parameters, such as the Fuchssteiner–Fokas–Camassa–Holm (ℱ ℱ ℋ) equation, the Rosenau–Hyman (ℛ ℋ) equation, and the Fornberg–Whitham (ℱ ) equation. The Sardar sub-equation and He's variational iteration techniques are employed to construct novel and accurate solitary wave solutions of the handled model. The obtained solutions are explained through some distinct graphs in contour, three-, two-dimensional. The research value is explained by comparing our results with some recently published studies. The employed methods show their simple, direct, effectiveness and their ability for handling many nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The Sharma–Tasso–Olver (STO) equation is a nonlinear, double-dispersive, partial differential equation that is physically important because it provides insights into the behavior of nonlinear waves and solitons in various physical areas, including fluid dynamics, optical fibers, and plasma physics. In this paper, the STO equation is generalized to a fractional equation by using Atangana (or Atangana–Baleanu) fractional space and time beta-derivatives since they have been found to be useful as a model for a variety of traveling-wave phenomena. Exact solutions are obtained for the integer-order and fractional-order equations by using the Sardar subequation method and an appropriate traveling-wave transformation. The exact solutions are obtained in terms of generalized trigonometric and hyperbolic functions. The exact solutions are derived for the integer-order STO and for a range of values of fractional orders. Numerical solutions are also obtained for a range of parameter values for both the fractional and integer orders to show some of the types of solutions that can occur. As examples, the solutions are obtained showing the physical behavior, such as the solitary wave solutions of the singular kink-type and periodic wave solutions. The results show that the Sardar subequation method provides a straightforward and efficient method for deriving new exact solutions for fractional nonlinear partial differential equations of the STO type. [ABSTRACT FROM AUTHOR]